We analyze flow in a heterogeneous aquifer composed of different geologic facies, whose hydraulic properties and internal geometries are uncertain. Our analysis employs random domain decomposition to derive robust moment equations for flow in composite porous media. The approach accounts explicitly for the multi-scale effects of material and geometric uncertainties on the ensemble moments of head and flux. We use an indicator-based geostatistical methodology to estimate the facies geometries and to quantify the corresponding uncertainty. We then apply our approach to a synthetic flow example, where stratigraphic and sedimentological data from a real aquifer are used to obtain the probabilistic facies distribution. We solve the equations for ensemble moments of hydraulic head and study the impact of unknown geometry of materials on the statistical moments of head.